Cambridge A Level Physics 9702 — 2011 Oct/Nov Paper 3 · Variant 3

1 In this experiment you will determine the resistivity of a metal in the form of a wire. (a) (i) Measure and record the diameter d of the short sample of wire that is attached to the card. You may remove the wire from the card. d = ................................................. [1] (ii) Calculate the cross-sectional area A of the wire, in m2, using the formula π d 2 A = . 4 A = ................................................. m2 (b) (i) Using the wire that is taped to the metre rule, set up the circuit shown in Fig. 1.1. Close the switch. d.c. power supply R R metre rule Y l V Fig. 1.1 (ii) Position the crocodile clip Y approximately half-way along the wire. (iii) Measure and record the length l of wire between the two crocodile clips and the voltmeter reading V. l = ...................................................... V = ...................................................... [1] (c) By moving crocodile clip Y, change l and repeat (b)(iii) until you have six sets of readings For 1 1 Examiner’s of l and V for l 20 cm. Include values of and in your table. l V Use [10] 1 1(d) (i) Plot a graph of on the y-axis against on the x-axis. [3] V l (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ...................................................... y-intercept = ...................................................... [2] For Examiner’s Use (e) The quantities V and l are related by the equation For Examiner’s 1 M Use = + N V l where M and N are constants. (i) Use your answers in (d)(iii) to determine values for M and N. M = ............................................. m V–1 N = ................................................ V–1 [1] (ii) The resistivity ρ of the material of the wire, in Ω m, can be found using the relationship 5 A N ρ = . M Using your answers in (e)(i) and (a)(ii), calculate a value for ρ. ρ = .......................................... Ω m [1] You may not need to use all of the materials provided. For Examiner’s Use

Mark scheme: 1 (a) (i) All raw values of d in the range 0.15 mm ≤ d ≤ 0.40 mm to 0.01 mm with unit, or supervisor's value ± 0.10 mm [1] (b) (iii) l and V with unit. Value of l in the range 40.0 cm ≤ l ≤ 60.0 cm. [1] (c) Six sets of readings of l and V scores 5 marks, five sets scores 4 marks etc. Incorrect trend –1. Major help from supervisor –2. Minor help from supervisor –1. [5] Range of l: ∆l ≥ 50 cm. [1] Column headings: [1] Each column heading must contain a quantity and a unit where appropriate. There must be some distinguishing mark between the quantity and the unit, e.g. 1/V / V–1. Accept 1/V (V–1) but do not allow 1/V (V)–1 or 1/l (m). Consistency of presentation of raw readings: [1] All values of raw l must be given to 0.001 m. Significant figures: [1] Significant figures for 1/ V must be to the same as, or one more than, the least number of significant figures used in raw V. Calculation: 1/ V calculated correctly. [1] (d) (i) Axes: [1] Sensible scales must be used. Awkward scales (e.g. 3:10) are not allowed. Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Scales must be labelled with the quantity which is being plotted. Scale markings must be no more than three large squares apart. Plotting of points: [1] All observations in the table must be plotted. Check that the points are correctly plotted. Work to an accuracy of half a small square in both the x and y directions. Do not accept ‘blobs’ (points with diameter greater than half a small square). Quality: [1] All points in the table must be plotted (at least 5) for this mark to be scored. Scatter of points must be less than ± 0.2 m–1 (0.002 cm–1) of 1/l of a straight line. (ii) Line of best fit: [1] Judge by balance of all the points on the grid (at least 5) about the candidate's line. There must be an even distribution of points either side of the line along the full length. Allow one anomalous point only if clearly indicated (i.e. circled or labelled) by the candidate. GCE AS/A LEVEL – October/November 2011 9702 33 (d) (iii) Gradient: [1] The hypotenuse of the triangle used must be at least half the length of the drawn line. Both read-offs must be accurate to half a small square in both x and y directions. The method of calculation must be correct. Intercept: [1] Either: Check correct read-off from a point on the line and substitution into y = mx + c. Read-off must be accurate to half a small square in both x and y directions. Allow ecf of gradient value. Or: Check the read-off of the intercept directly from the graph. (e) (i) M = value of gradient, N = value of y-intercept. [1] (ii) Substitution into equation and answer for ρ in range 2 – 20 × 10–7 Ω m (0.2 × 10–6 – 2 × 10–6 Ω m). [1] [Total: 20]

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2 In this experiment you will investigate how the motion of a metre rule depends on the length of the string loops used to suspend it. (a) Measure and record the width w of one of the metre rules, as shown in Fig. 2.1. w Fig. 2.1 w = ............................................ cm [1] (b) (i) Select the two longer pieces of string. (ii) Tie the ends of one piece of string to make a loop. (iii) Measure and record the length l of this loop, as shown in Fig. 2.2. l Fig. 2.2 l = ................................................. [1] (iv) Repeat (ii) with the other long piece of string. The length of this loop should be the same as that in (iii). (c) (i) Use the stands to set up the two metre rules and the two loops of string as shown For in Fig. 2.3. Examiner’s Use clamp metre rule loop loop d metre rule stand bench Fig. 2.3 The rules should be horizontal with the scale markings facing you. The loops should be vertical, parallel to each other and placed at the 5 cm and 95 cm marks on both rules. (ii) Using your values in (a) and (b)(iii), determine the distance d using the relationship d = l – 2w. d = ................................................. [1] (iii) Estimate the percentage uncertainty in your value of d. percentage uncertainty = ................................................. [1] (d) Move the left end of the bottom rule towards you and the right end away from you. For Release the rule and watch the movement. Examiner’s The left end of the rule will move away from you and back towards you, completing a Use swing. The time taken for one complete swing is T. By timing several of these complete swings, determine an accurate value for T. T = .............................................. s [2] (e) Repeat (b), (c)(i), (c)(ii) and (d) for the shorter lengths of string. l = ................................................. [1] d = ...................................................... T = ............................................... s [2]

Mark scheme: 2 (a) Measurement of all raw w to nearest mm in range 2.0 ≤ w ≤ 3.5 cm. [1] (b) (iii) Value of l in range 25 cm ≤ l ≤ 50 cm with unit. [1] (c) (ii) Correct calculation of d. Write in correct value if incorrect. Unit not needed. [1] (iii) Absolute uncertainty in d in the range 3–15 mm (but if repeated readings have been taken then the absolute uncertainty could be half the range, unless zero). Correct method shown used to find the percentage uncertainty. [1] (d) Value of T in range 0.3 s < T <1.5 s. [1] Evidence of repeats. [1] (e) Second value of l. [1] Second value of T. [1] Second value of T < first value of T. [1] (f) (i) Two values of k calculated correctly. [1] (ii) Justification of s.f. in k linked to time AND d or l. [1] (iii) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. [1] GCE AS/A LEVEL – October/November 2011 9702 33 (g) (i) Limitations 4 max. (ii) Improvements 4 max. Do not credit A Two readings are not enough Take more readings and plot ‘Few readings’/‘take more (to draw a conclusion) a graph/ readings and calculate calculate more k values (and average k’/‘only one reading’ compare) B Loops not the same size/ Method to ensure loops same Difficult to tie knots ruler(s) not horizontal/ size, e.g. use glue or tape to Use of spirit level/use of secure ends plumbline together/tie around fixed Rubber bands or other points/template/mark string material Use of Blu-Tack String stretching C Difficult to judge end/start/ Use of fiducial marker/pointer Reaction time error centre of swing/difficult to Human reaction judge complete swing Difficult to know when to start/ stop timer D Irregular/uneven/unusual Method of ensuring correct Fans/switch off fans swings/not in same horizontal release, e.g. (two) stop(s) at Amplitude changes plane/centre of bottom rule either end not fixed E Loops slide Method, e.g. glue, tape to ‘Glue’ or ‘tape’ on its own fix loop to rule/ drill hole to attach string/ make grooves to hold string F T or time short/large Improved method of timing, Use of computer uncertainty in T e.g. video and timer/frame-by- Light gates frame/increase d or l, Camera decrease distance between High speed camera loops, correct position of Too fast motion sensor linked to data Time too fast logger Time more swings Time large no. of swings. G Reason for calculation of d Measure d directly/measure w Parallax error inaccurate, e.g. different w/ for both rules/measure and Use of set squares thickness of rule not taken allow for thickness. Vernier callipers into account Just ‘different w’ [Total: 20]

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